Noninteger‐Polynomial Flnite‐Element Analysis of Column Buckling

Polynomials with integer powers have been used with the Rayleigh-Ritz method and the finite-element method for the computation of approximate buckling loads, natural frequencies, static deflection, etc. However, there is an improved version of the Rayleigh method, in which the leading exponent of the polynomial is initially undetermined rather than being an integer. Since the Rayleigh method yields an upper bound, the exponent is optimized to yield a minimum result. In the present work, this concept is applied to the finite-elementanalysis of column buckling. For purposes of evaluation, the approximate results were compared to closed-form solutions where possible. The improvement in accuracy over the classical finite-element method was quite significant.